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The integration of renewable energy sources (RES) has facilitated efficient and sustainable resource allocation for wireless communication systems. In this paper, a novel framework is introduced to develop coordinated multicell beamforming (CMBF) design for wireless cellular networks powered by a smart microgrid, where the BSs are equipped with RES harvesting devices and can perform two-way (i.e., buying/selling) energy trading with the main grid. To this end, new models are put forth to account for the stochastic RES harvesting, two-way energy trading, and conditional value-at-risk (CVaR) based energy transaction cost. Capitalizing on these models, we propose a distributed CMBF solution to minimize the grid-wide transaction cost subject to user quality-of-service (QoS) constraints. Specifically, relying on state-of-the-art optimization tools, we show that the relevant task can be formulated as a convex problem that is well suited for development of a distributed solver. To cope with stochastic availability of the RES, the stochastic alternating direction method of multipliers (ADMM) is then leveraged to develop a novel distributed CMBF scheme. It is established that the proposed scheme is guaranteed to yield the optimal CMBF solution, with only local channel state information available at each BS and limited information exchange among the BSs. Numerical results are provided to corroborate the merits of the proposed scheme.